x^2-7x-18=9

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Solution for x^2-7x-18=9 equation: 


Simplifying
x2 + -7x + -18 = 9

Reorder the terms:
-18 + -7x + x2 = 9

Solving
-18 + -7x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-18 + -9 + -7x + x2 = 9 + -9

Combine like terms: -18 + -9 = -27
-27 + -7x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-27 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -7x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -7x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -7x + x2 = 0 + 27
-7x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-7x + x2 = 27

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 27 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 27 + 12.25

Combine like terms: 27 + 12.25 = 39.25
12.25 + -7x + x2 = 39.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
x + -3.5 = 6.264982043

Simplifying
x + -3.5 = 6.264982043

Reorder the terms:
-3.5 + x = 6.264982043

Solving
-3.5 + x = 6.264982043

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 6.264982043 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.264982043 + 3.5
x = 6.264982043 + 3.5

Combine like terms: 6.264982043 + 3.5 = 9.764982043
x = 9.764982043

Simplifying
x = 9.764982043


Subproblem 2
x + -3.5 = -6.264982043

Simplifying
x + -3.5 = -6.264982043

Reorder the terms:
-3.5 + x = -6.264982043

Solving
-3.5 + x = -6.264982043

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -6.264982043 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.264982043 + 3.5
x = -6.264982043 + 3.5

Combine like terms: -6.264982043 + 3.5 = -2.764982043
x = -2.764982043

Simplifying
x = -2.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.764982043, -2.764982043}

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